This paper presents a nonlinear theory for sand drain consolidation of clayey soils under time dependent loading. The solution is obtained using the method of separation of variables. Using the solutions obtained, some diagrams are prepared and the relevant consolidation behavior of soil with vertical and horizontal drainage under time-loadings is discussed. For nonlinear material properties, average degree of consolidation can be defined either in terms of settlement or in terms of effective stress. And consolidation will be slower when compared to the cases with constant material properties. And the difference depends on the external loading pressure N, and the construction time Tvc.